I have to convert \({-14.8°}\) into radians, expressing my answer as exact values and as approximate measures (to the nearest hundredth of a radian).

This may be a very elementary question, but I'm not sure how express my answer in exact values?

I got \({-7.4 \over 90}π\) using the conversion factor of \({π \over 180°}\) and dividing \({-14.8°}\) and \({180°}\)by 2.

However, the textbook got \({-37π \over 450}\) . That means \( {2.5}\) was used to multiply \({-14.8°}\) and \({180°}\) . Why 2.5? How did the textbook get this number?

Thank you! :)

Guest Dec 3, 2018

#1**+2 **

I have to convert -14.8 degrees into radians, expressing my answer as exact values and as approximate measures (to the nearest hundredth of a radian).

\( \text{Not that the surtitle c is a symbol for radians. (not commonly used though)}\\180^\circ=\pi^c\\ 1^\circ=\frac{\pi^c}{180}\\ -14.8^\circ=\frac{-14.8\pi^c}{180}\\ -14.8^\circ=\frac{-148\pi^c}{1800}\\ -14.8^\circ=\frac{-37\pi}{450}\;\;radians\\ \)

.Melody Dec 3, 2018

#1**+2 **

Best Answer

I have to convert -14.8 degrees into radians, expressing my answer as exact values and as approximate measures (to the nearest hundredth of a radian).

\( \text{Not that the surtitle c is a symbol for radians. (not commonly used though)}\\180^\circ=\pi^c\\ 1^\circ=\frac{\pi^c}{180}\\ -14.8^\circ=\frac{-14.8\pi^c}{180}\\ -14.8^\circ=\frac{-148\pi^c}{1800}\\ -14.8^\circ=\frac{-37\pi}{450}\;\;radians\\ \)

Melody Dec 3, 2018